CAD tip # 13965:

End the incremental loop displaying the cumulative length by pressing [ESC]. Then the total length value (in the current document length units) is displayed for copying.

oPrecision = 4
Dim TotalLength As Double
Dim oSweep As SweepFeature
Dim oDoc = ThisDoc.Document
Dim oDef As PartComponentDefinition
oDef = oDoc.ComponentDefinition
Dim oHighLight As Inventor.HighlightSet
oHighLight = oDoc.CreateHighlightSet
On Error GoTo ExitRule
oUOM = oDoc.UnitsOfMeasure
oLUnits = oUOM.LengthUnits
oUnitString = oUOM.GetStringFromType(oLUnits)
Dim cnt As Integer = 0
Dim oPrompt As String 
oPrompt = "Select Sweeps, <‍ESC> to end..."

While True 'loop
 selectF = ThisApplication.CommandManager.Pick _
		(kPartFeatureFilter, oPrompt)
 If IsNothing(selectF) Then Exit While
 If TypeOf selectF Is SweepFeature Then
	oSweep = selectF
    Dim oProfileOrigin As Point2d
    oProfileOrigin = oSweep.Profile.RegionProperties.Centroid
    Dim oProfileOrigin3D As Point
    oProfileOrigin3D = oSweep.Profile.Parent.SketchToModelSpace(oProfileOrigin)
    Dim oCurves As ObjectsEnumerator
    oCurves = oDef.Features.SweepFeatures.GetTruePath(oSweep.Path, oProfileOrigin3D)
    Dim oCurve As Object
    For Each oCurve In oCurves
        Dim oCurveEval As CurveEvaluator
        oCurveEval = oCurve.Evaluator
        Dim MinParam As Double
        Dim MaxParam As Double
        Dim Length As Double
        Call oCurveEval.GetParamExtents(MinParam, MaxParam)
        Call oCurveEval.GetLengthAtParam(MinParam, MaxParam, Length)
        TotalLength = TotalLength + Length
    Next
	
	cnt = cnt + 1
	Call oHighLight.AddItem(selectF)
	oPrompt = Round(oUOM.ConvertUnits(TotalLength, "cm", _
			oLUnits), oPrecision) & " " & oUnitString
 End If
End While

InputBox("TOTAL LENGTH" & vbCrLf & "of " & cnt & " sweeps:", "Sweep Length", oPrompt)

ExitRule :
oHighLight.Clear

For possible bulk selection of ALL sweeps in the model, use the loop (instead of While True):

For Each oSweep In oDef.Features.SweepFeatures

Next